Visualizing Forecast Uncertainty¶
Effective forecasting involves more than just predicting a single future value; it requires understanding the inherent uncertainty surrounding that prediction. Point forecasts alone can be misleading, especially when making critical decisions based on them. k-diagram provides a suite of specialized polar visualizations designed to dissect and illuminate various facets of forecast uncertainty.
Why Polar Plots for Uncertainty?¶
Traditional Cartesian plots can become cluttered when visualizing multiple aspects of uncertainty across many data points or locations. k-diagram leverages the polar coordinate system to:
- Provide a compact overview of uncertainty characteristics
across the entire dataset (represented angularly).
- Highlight patterns in uncertainty related to temporal or
spatial dimensions (if mapped to the angle).
- Visually emphasize drift, anomalies, and coverage
in intuitive ways using radial distance and color.
This page details the functions within k-diagram focused on evaluating prediction intervals, diagnosing coverage failures, analyzing anomaly severity, and tracking how uncertainty evolves.
Summary of Uncertainty Functions¶
The following functions provide different perspectives on forecast uncertainty and related diagnostics:
Function |
Description |
|---|---|
Compares actual vs. predicted point values point-by-point. |
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Visualizes magnitude and type of prediction anomalies. |
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Calculates and plots overall interval coverage scores. |
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Diagnoses interval coverage point-by-point on a polar plot. |
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Shows consistency/variability of interval widths over time. |
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Visualizes the width of prediction intervals across samples. |
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Tracks how average uncertainty width changes over horizons. |
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General plot for visualizing multiple series (e.g., quantiles). |
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Visualizes drift of uncertainty using concentric rings over time. |
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Shows the rate of change (velocity) of median predictions. |
Detailed Explanations¶
Let’s explore some of these functions in detail.
Actual vs. Predicted Comparison (plot_actual_vs_predicted())¶
Purpose: This plot provides a direct visual comparison between the actual observed ground truth values and the model’s point predictions (typically the median forecast, Q50) for each sample or location. It’s a fundamental diagnostic for assessing basic model accuracy and identifying systematic biases.
Mathematical Concept: For each data point \(i\), we have an actual value \(y_i\) and a predicted value \(\hat{y}_i\). The plot displays both values radially at a corresponding angle \(\theta_i\). The difference, or error, \(e_i = y_i - \hat{y}_i\), is implicitly visualized by the gap between the plotted points/lines for actual and predicted values. Often, gray lines connect \(y_i\) and \(\hat{y}_i\) at each angle to emphasize the error magnitude and direction.
Interpretation:
- Closeness: How close are the points or lines representing actual
and predicted values? Closer alignment indicates better point-forecast accuracy.
- Systematic Bias: Does the prediction line/dots consistently sit
inside or outside the actual line/dots? This indicates a systematic under- or over-prediction bias.
- Error Magnitude: The length of the connecting gray lines (if shown)
or the radial distance between points directly shows the prediction error for each sample. Large gaps indicate poor predictions for those points.
- Angular Patterns: If the angle \(\theta\) represents a meaningful
dimension (like time index, season, or spatial grouping), look for patterns in accuracy or bias around the circle. Does the model perform better or worse at certain “angles”?
Use Cases:
- Initial Performance Check: Get a quick overview of how well the
point forecast aligns with reality across the dataset.
Bias Detection: Easily spot systematic over- or under-prediction.
- Identifying Problematic Regions: If using angles meaningfully,
locate specific periods or areas where point predictions are poor.
- Communicating Basic Accuracy: Provides a simple visual for
stakeholders before diving into complex uncertainty measures.
Advantages of Polar View:
Provides a compact, circular overview of performance across many samples.
- Can make cyclical patterns (if angle relates to time, like month or
hour) more apparent than a standard time series plot.
Example: (See Gallery for code and plot examples)
Anomaly Magnitude Analysis (plot_anomaly_magnitude())¶
Purpose: This diagnostic specifically focuses on prediction interval failures. It identifies instances where the actual observed value falls outside the predicted range [Qlow, Qup] and visualizes the location, type (under- or over-prediction), and severity (magnitude) of these anomalies. It answers: “When my model’s uncertainty bounds are wrong, how wrong are they, and where?”
Mathematical Concept: An anomaly exists if the actual value \(y_i\) is outside the interval defined by the lower (\(Q_{low,i}\)) and upper (\(Q_{up,i}\)) quantiles.
Under-prediction: \(y_i < Q_{low,i}\)
Over-prediction: \(y_i > Q_{up,i}\)
The magnitude (\(r_i\)) of the anomaly is the absolute distance from the actual value to the nearest violated bound:
Only points where \(r_i > 0\) are plotted. The radial coordinate of a plotted point is \(r_i\).
Interpretation:
- Presence/Absence: Points only appear if an anomaly occurred. A sparse
plot indicates good interval coverage. Dense clusters indicate regions of poor uncertainty estimation.
- Radius: The distance from the center directly represents the
severity of the anomaly. Points far from the center are large errors relative to the predicted bounds.
- Color: Distinct colors (e.g., blues for under-prediction, reds for
over-prediction) immediately classify the type of failure. Color intensity often also maps to the magnitude \(r_i\).
- Angular Position: Shows where (which samples, locations, or times,
based on the angle representation) these failures occur. Look for clustering at specific angles.
Use Cases:
- Risk Assessment: Identify predictions where the actual outcome might
be significantly worse than the uncertainty bounds suggested.
- Model Calibration Check: Assess if the prediction intervals are
meaningful. Frequent or large anomalies suggest poor calibration.
- Pinpointing Failure Modes: Determine if the model tends to fail more
by under-predicting or over-predicting, and under what conditions (angles).
- Targeting Investigation: Guide further analysis or data collection
efforts towards the specific samples/locations exhibiting the most severe anomalies.
Advantages of Polar View:
Provides a focused view solely on prediction interval failures.
Radial distance intuitively maps to error magnitude/severity.
Color effectively separates under- vs. over-prediction types.
- Circular layout helps identify patterns or concentrations of anomalies
across the angular dimension.
Example: (Refer to Gallery and runnable code examples)
Overall Coverage Scores (plot_coverage())¶
Purpose: This function calculates and visualizes the overall empirical coverage rate for one or more sets of predictions. It answers the fundamental question: “Across the entire dataset, what fraction of the time did the true observed values fall within the specified prediction interval bounds (e.g., Q10 to Q90)?” It allows for comparing this aggregate performance across different models or prediction sets using various chart types.
Mathematical Concept: The empirical coverage for a given prediction interval \([Q_{low,i}, Q_{up,i}]\) and actual values \(y_i\) over \(N\) samples is calculated as:
Where \(\mathbf{1}\{\cdot\}\) is the indicator function, which is 1 if the condition (actual value \(y_i\) is within the bounds) is true, and 0 otherwise.
For point predictions \(\hat{y}_i\), coverage typically measures exact matches (often resulting in very low scores unless data is discrete): \(\text{Coverage} = \frac{1}{N} \sum_{i=1}^{N} \mathbf{1}\{y_i = \hat{y}_i\}\).
Interpretation:
- Compare to Nominal Rate: The primary use is to compare the
calculated empirical coverage rate against the nominal coverage rate implied by the quantiles used. For example, a Q10-Q90 interval has a nominal coverage of 80% (0.8). * If Empirical Coverage ≈ Nominal Coverage: The intervals are well-
calibrated on average.
- If Empirical Coverage > Nominal Coverage: The intervals are too wide
(conservative) on average.
- If Empirical Coverage < Nominal Coverage: The intervals are too narrow
(overconfident) on average.
- Model Comparison: When plotting multiple models, directly compare
their coverage scores. A model closer to the nominal rate is generally better calibrated in terms of its average interval performance.
- Chart Type:
bar or line: Good for direct comparison of scores between models.
- pie: Shows the proportion of coverage relative to the sum (less common
for direct calibration assessment).
- radar: Provides a profile view comparing multiple models across the
same metric (coverage).
Use Cases:
- Quickly assessing the average calibration of prediction intervals for
one or multiple models.
- Comparing the overall reliability of uncertainty estimates from different
forecasting methods.
Summarizing interval performance for reporting.
Advantages:
- Provides a single, easily interpretable summary statistic for average
interval performance per model.
- Offers multiple visualization options (kind parameter) for flexible
comparison.
Example: (See Gallery for code and plot examples)
Point-wise Coverage Diagnostic (plot_coverage_diagnostic())¶
Purpose:
While plot_coverage() gives an overall
average, this function provides a granular, point-by-point diagnostic
of prediction interval coverage on a polar plot. It visualizes where
(at which specific sample, location, or time, represented angularly)
the prediction intervals succeeded or failed to capture the actual value.
Mathematical Concept: For each data point \(i\), a binary coverage indicator \(c_i\) is calculated:
Each point \(i\) is then plotted at an angle \(\theta_i\) (determined by its index or an optional feature) and a radius \(r_i = c_i\). This means:
Covered points (\(c_i=1\)) are plotted at radius 1.
Uncovered points (\(c_i=0\)) are plotted at radius 0.
The plot also typically shows the overall coverage rate \(\bar{c} = \frac{1}{N} \sum c_i\) as a prominent reference circle.
Interpretation:
- Radial Position: Instantly separates successes (radius 1) from
failures (radius 0).
- Angular Clusters: Look for clusters of points at radius 0. Such
clusters indicate specific regions, times, or conditions (depending on what the angle represents) where the model’s prediction intervals systematically fail. Randomly scattered points at radius 0 suggest less systematic issues.
- Average Coverage Line: The solid circular line drawn at radius
\(\bar{c}\) represents the overall empirical coverage rate. Compare its position to: * The nominal coverage rate (e.g., 0.8 for an 80% interval). * Reference grid lines (often shown at 0.2, 0.4, 0.6, 0.8, 1.0).
- Background Gradient (Optional): If enabled, the shaded gradient
extending from the center to the average coverage line provides a strong visual cue for the overall performance level.
- Point/Bar Color: Color (e.g., green for covered, red for uncovered
using the default ‘RdYlGn’ cmap) reinforces the binary status.
Use Cases:
- Diagnosing Coverage Failures: Go beyond the average rate to see
where and how often intervals fail.
- Identifying Systematic Issues: Detect if failures are concentrated
in specific segments of the data (angles).
- Visual Calibration Assessment: Provides a more intuitive feel for
calibration than just a single number. Is the coverage rate met because most points are covered, or are there many failures balanced by overly wide intervals elsewhere?
- Debugging Model Uncertainty: Pinpoint areas needing improved
uncertainty quantification.
Advantages (Polar Context):
Excellent for visualizing the status of many points compactly.
- The radial mapping (0 or 1) provides a very clear visual separation
of coverage success/failure.
Angular clustering of failures is easily identifiable.
- The average coverage line acts as an immediate visual benchmark against
the plot boundaries (0 and 1) and reference grid lines.
Example: (See Gallery or function docstring for code and plot examples)
Interval Width Consistency (plot_interval_consistency())¶
Purpose: This plot analyzes the temporal stability of the predicted uncertainty range. It visualizes how much the width of the prediction interval (\(Q_{up} - Q_{low}\)) fluctuates for each location or sample across multiple time steps or forecast horizons. It answers: “Are the model’s uncertainty estimates stable over time for a given location, or do they vary wildly?”
Mathematical Concept: For each location/sample \(j\), the interval width is calculated for each available time step \(t\):
The plot then visualizes the variability of these widths \(w_{j,t}\) over the time steps \(t\) for each location \(j\). The radial coordinate \(r_j\) typically represents either:
Standard Deviation: \(r_j = \sigma_t(w_{j,t})\) - Measures the absolute variability of the width.
Coefficient of Variation (CV): \(r_j = \frac{\sigma_t(w_{j,t})}{\mu_t(w_{j,t})}\) - Measures the relative variability (standard deviation relative to the mean width). Set via the
use_cv=Trueparameter.
Each location \(j\) is plotted at an angle \(\theta_j\) (based on index) and radius \(r_j\). The color of the point often represents the average median prediction \(\mu_t(Q_{50,j,t})\) across the time steps, providing context.
Interpretation:
- Radius: Points far from the center indicate locations where the
prediction interval width is inconsistent or varies significantly across the different time steps/horizons considered. Points near the center have stable interval width predictions over time.
- CV vs. Standard Deviation (`use_cv`):
- If use_cv=False (default), radius shows absolute standard
deviation. A large radius means large absolute fluctuations in width.
- If use_cv=True, radius shows relative variability (CV). A large
radius means the width fluctuates significantly compared to its average width. This helps compare consistency across locations that might have very different average interval widths.
- Color (Context): If q50_cols are provided, color typically shows
the average Q50 value. This helps answer questions like: “Does high inconsistency (large radius) tend to occur in locations with high or low average predicted values?”
- Angular Clusters: Clusters of points with high/low radius might indicate
spatial patterns in the stability of uncertainty predictions.
Use Cases:
- Assessing Model Reliability Over Time: Identify locations where
uncertainty estimates are unstable across forecast horizons.
- Diagnosing Temporal Effects: Understand if interval predictions
become more or less variable further into the future.
- Comparing Relative vs. Absolute Stability: Use use_cv to
distinguish between large absolute fluctuations and large relative fluctuations.
- Identifying Locations for Scrutiny: Points with high inconsistency
might warrant further investigation into why the uncertainty estimate is so variable for those locations/conditions.
Advantages (Polar Context):
Compactly displays the consistency profile across many locations.
- Radial distance provides an intuitive measure of inconsistency
(variability).
Allows visual identification of clusters based on consistency levels.
- Color adds valuable context about the average prediction level associated
with different consistency levels.
Example: (See Gallery or function docstring for code and plot examples)
Prediction Interval Width Visualization (plot_interval_width())¶
Purpose: This function creates a polar scatter plot focused solely on the magnitude of predicted uncertainty. It visualizes the width of the prediction interval (\(Q_{up} - Q_{low}\)) for each individual sample or location, typically at a single snapshot in time or for a specific forecast horizon. It answers: “How wide is the predicted uncertainty range for each point in my dataset?”
Mathematical Concept: For each data point \(i\), the interval width is calculated:
The point is plotted at an angle \(\theta_i\) (based on index) and a
radius \(r_i = w_i\). Optionally, a third variable \(z_i\)
from a specified z_col can determine the color of the point; otherwise,
the color typically represents the width \(w_i\) itself.
Interpretation:
- Radius: The radial distance directly corresponds to the width of
the prediction interval. Points far from the center represent samples with high predicted uncertainty (wide intervals). Points near the center have low predicted uncertainty (narrow intervals).
- Color (with `z_col`): If a
z_col(e.g., the median prediction Q50, or the actual value) is provided, the color allows you to see how interval width relates to that variable. For example, are wider intervals (larger radius) associated with higher or lower median predictions (color)?
- Color (with `z_col`): If a
- Color (without `z_col`): If no
z_colis given, color usually maps to the width itself, reinforcing the radial information.
- Color (without `z_col`): If no
- Angular Patterns: Look for regions around the circle (representing
subsets of data based on index order or a future theta_col implementation) that exhibit consistently high or low interval widths.
Use Cases:
- Identifying samples or locations with the largest/smallest predicted
uncertainty ranges at a specific time/horizon.
- Visualizing the overall distribution of uncertainty magnitudes across
the dataset.
- Exploring potential relationships between uncertainty width and other
factors (e.g., input features, predicted value magnitude) by using the
z_coloption.
- Assessing if uncertainty is relatively uniform or highly variable
across samples.
Advantages (Polar Context):
Provides a compact overview of uncertainty magnitude for many points.
- The radial distance offers a direct, intuitive mapping for interval
width.
- Facilitates the visual identification of angular patterns or clusters
related to uncertainty levels.
- Allows simultaneous visualization of location (angle), uncertainty
width (radius), and a third variable (color via
z_col).
Example: (See Gallery or function docstring for code and plot examples)
Model Forecast Drift (plot_model_drift())¶
Purpose: This visualization focuses on model degradation over forecast horizons. It creates a polar bar chart to show how the average prediction uncertainty (specifically, the mean interval width \(\mathbb{E}[Q_{up} - Q_{low}]\)) changes as the forecast lead time increases. It helps diagnose concept drift or model aging effects related to uncertainty.
Mathematical Concept: For each distinct forecast horizon \(h\) (e.g., 1-step ahead, 2-steps ahead), the average interval width across all \(N\) samples is calculated:
Each horizon \(h\) is assigned a distinct angle \(\theta_h\) on
the polar plot. A bar is drawn at this angle with a height (radius)
proportional to the average width \(\bar{w}_h\). The color of the
bar typically also reflects this average width, or potentially another
aggregated metric for that horizon if color_metric_cols is used.
Interpretation:
- Radial Growth: The key aspect is the change in bar height (radius)
as the angle (horizon) progresses. A noticeable increase in radius for later horizons indicates that, on average, the model’s prediction intervals widen significantly as it forecasts further into the future. This signifies increasing uncertainty or model drift.
- Bar Height Comparison: Directly compare the heights of bars for
different horizons to quantify the average increase in uncertainty. Annotations usually display the exact average width \(\bar{w}_h\) for each horizon.
- Stability: Bars of relatively similar height across horizons suggest
that the model’s average uncertainty level is stable over the forecast lead times considered.
Use Cases:
- Detecting Model Degradation: Identify if forecast uncertainty grows
unacceptably large at longer lead times.
- Assessing Forecast Reliability Horizon: Determine the practical
limit of how far ahead the model provides reasonably certain forecasts.
- Informing Retraining Strategy: Significant drift might indicate the
need for more frequent model retraining or incorporating features that capture evolving dynamics.
- Comparing Model Stability: Generate plots for different models to
compare how their uncertainty characteristics drift over time.
Advantages (Polar Context):
- The polar bar chart format makes the “outward drift” of average
uncertainty across increasing horizons (angles) very intuitive to grasp.
- Provides a concise summary comparing average uncertainty levels across
multiple forecast lead times.
Example: (See Gallery or function docstring for code and plot examples)
General Polar Series Visualization (plot_temporal_uncertainty())¶
Purpose: This is a general-purpose polar scatter plot utility within the uncertainty module, designed for visualizing and comparing multiple data series (columns from a DataFrame) simultaneously. While flexible, a common application in uncertainty analysis is to plot different quantile predictions (e.g., Q10, Q50, Q90) for the same forecast horizon to visualize the uncertainty spread at that specific point in time across all samples.
Mathematical Concept:
For each data series \(k\) (corresponding to a column in q_cols)
and each sample \(i\), the value \(v_{i,k}\) is plotted at an
angle \(\theta_i\) (based on index) and radius \(r_{i,k} = v_{i,k}\).
If normalize=True, each series \(k\) is independently scaled
to the range [0, 1] before plotting using min-max scaling:
\(r_{i,k} = (v_{i,k} - \min_j(v_{j,k})) / (\max_j(v_{j,k}) - \min_j(v_{j,k}))\).
Each series \(k\) is assigned a distinct color.
Interpretation:
- Series Comparison: Observe the relative radial positions of points
belonging to different series (colors) at the same angle.
- Uncertainty Spread (Quantile Use Case): When plotting Q10, Q50,
and Q90 for a single horizon: * The radial distance between the points for Q10 (e.g., blue) and
Q90 (e.g., red) at a specific angle represents the interval width (uncertainty) for that sample.
Look for how this spread varies around the circle (across samples).
- The position of the Q50 points (e.g., green) shows the central tendency
relative to the bounds.
- Normalization Effect: If
normalize=True, the plot emphasizes the relative shapes and overlap of the series, regardless of their original scales. This is useful for comparing patterns but loses information about absolute magnitudes. If
normalize=False, the radial axis reflects the actual data values.
- Normalization Effect: If
- Angular Patterns: Observe if specific series tend to be higher or lower
at certain angles (samples/locations).
Use Cases:
- Visualizing Uncertainty Intervals: Plot Qlow, Qmid, Qup for a single
time step/horizon to see the uncertainty band across samples.
- Comparing Multiple Models: Plot the point predictions (e.g., Q50)
from several different models to compare their outputs side-by-side.
- Plotting Related Variables: Visualize any set of related numerical
columns from your DataFrame in a polar layout.
Advantages (Polar Context):
Allows overlaying multiple related data series in a single, compact plot.
- Effective for visualizing the spread or range between different
series (like quantiles) at each angular position.
- Normalization option facilitates shape comparison for series with
different scales.
Can reveal shared cyclical patterns among the plotted series.
Example: (See Gallery or function docstring for code and plot examples)
Multi-Time Uncertainty Drift Rings (plot_uncertainty_drift())¶
Purpose:
This plot offers a dynamic view of how the spatial pattern of
prediction uncertainty (interval width) evolves across multiple time
steps (e.g., years) for all locations simultaneously. Unlike
plot_model_drift(), which averages
across locations for each horizon, this function plots each time step
as a distinct concentric ring, allowing direct comparison of the
uncertainty “map” at different times.
Mathematical Concept: For each location \(j\) and time step \(t\), the interval width is calculated: \(w_{j,t} = Q_{up,j,t} - Q_{low,j,t}\). These widths are typically normalized globally across all locations and times: \(w'_{j,t} = w_{j,t} / \max_{j',t'}(w_{j',t'})\).
Each location \(j\) corresponds to an angle \(\theta_j\). For a given time step \(t\), the radius \(r_{j,t}\) for location \(j\) is determined by a base offset for that ring plus the scaled normalized width:
Where \(R_t\) is the base radius for ring \(t\) (increasing
with time, controlled by base_radius) and \(H\) is a scaling
factor (band_height) controlling the visual impact of the width.
Each ring \(t\) receives a distinct color from the specified
cmap.
Interpretation:
- Concentric Rings: Each colored ring represents a specific time
step, with inner rings typically corresponding to earlier times and outer rings to later times.
- Ring Shape & Radius Variations: The deviations of a single ring
from a perfect circle show the spatial variability of uncertainty at that specific time step. Points on a ring that bulge outwards represent locations with higher relative uncertainty (wider intervals) at that time.
- Comparing Rings: Examine how the overall radius and “bumpiness”
change from inner rings (earlier times) to outer rings (later times). If outer rings are consistently larger or more irregular, it suggests that uncertainty generally increases and/or becomes more spatially variable over time.
- Angular Patterns: Trace specific angles (locations) across multiple
rings. Does the radius consistently increase (growing uncertainty at that location)? Is it consistently large or small (persistently high/low uncertainty location)?
Use Cases:
- Tracking the full spatial pattern of uncertainty as it evolves
over multiple forecast periods.
- Identifying specific locations where uncertainty grows or shrinks most
dramatically over time.
- Comparing the uncertainty landscape between different forecast horizons
(e.g., visualizing the difference in uncertainty patterns between a 1-year and a 5-year forecast).
- Complementing
plot_model_drift()by showing detailed spatial variations instead of just the average trend.
- Complementing
Advantages (Polar Context):
- Uniquely effective at overlaying multiple temporal snapshots of the
uncertainty field in a single, comparative view.
Concentric rings provide clear visual separation between time steps.
- Radial variations within each ring clearly highlight spatial differences
in relative uncertainty at that time.
Color coding aids in distinguishing and tracking specific time steps.
Example: (See Gallery or function docstring for code and plot examples)
Prediction Velocity Visualization (plot_velocity())¶
Purpose: This plot visualizes the rate of change, or velocity, of the central forecast prediction (typically the median, Q50) over consecutive time periods for each individual location or sample. It helps understand the predicted dynamics of the phenomenon being forecast, answering: “How fast is the predicted median value changing from one period to the next at each location?”
Mathematical Concept: For each location \(j\), the change in the median prediction between consecutive time steps \(t\) and \(t-1\) is calculated: \(\Delta Q_{50,j,t} = Q_{50,j,t} - Q_{50,j,t-1}\). The average velocity for location \(j\) over all time steps is the mean of these changes:
The point for location \(j\) is plotted at angle \(\theta_j\)
(based on index) and radius \(r_j = v_j\). The radius can be
normalized to [0, 1] if normalize=True. The color of the point can
represent either the velocity \(v_j\) itself, or the average
absolute magnitude of the Q50 predictions
\(\mathbb{E}_t [ |Q_{50,j,t}| ]\) (controlled by use_abs_color).
Interpretation:
- Radius: Directly represents the average velocity (rate of change)
of the Q50 prediction. * Points far from the center indicate locations with **high average
velocity** (rapidly changing predictions).
- Points near the center indicate locations with **low average
velocity** (stable predictions).
If normalized, the radius shows relative velocity across locations.
- Color (Mapped to Velocity): If
use_abs_color=False, color directly reflects the velocity value \(v_j\). Using a diverging colormap (like ‘coolwarm’) helps distinguish between positive average change (e.g., red/warm colors for increasing values) and negative average change (e.g., blue/cool colors for decreasing values).
- Color (Mapped to Velocity): If
- Color (Mapped to Q50 Magnitude): If
use_abs_color=True, color shows the average absolute value of the Q50 predictions themselves. This provides context: Is high velocity (large radius) associated with high or low absolute predicted values (color)?
- Color (Mapped to Q50 Magnitude): If
- Angular Patterns: Look for clusters of points with similar radius
(velocity) or color at specific angles, which might indicate spatial patterns in the predicted dynamics.
Use Cases:
- Identifying spatial “hotspots” where the predicted phenomenon is changing
most rapidly.
Locating areas of predicted stability or stagnation.
- Analyzing and visualizing the spatial distribution of predicted trends or
rates of change.
- Contextualizing velocity with the underlying magnitude of the prediction
(e.g., are flood level predictions rising faster in already high areas?).
Advantages (Polar Context):
- Provides a compact overview comparing the rate of change across many
locations or samples.
- Radial distance gives an intuitive sense of the magnitude of change
(velocity).
- Color adds a critical second layer of information, either directional change
or contextual magnitude.
- Facilitates spotting spatial patterns or clusters related to the dynamics
of the prediction.
Example: (See Gallery or function docstring for code and plot examples)